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Choose wisely. There is only one correct answer to each question.

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1.
Which type of fund makes a good core investment for most investors?
Choose wisely. There is only one correct answer.
A large-cap blend fund. Your core funds should be your portfolio anchors, the funds you rely on to reach your goals. For many, large-cap funds fill the bill. Emerging-markets and tech funds are too risky to be at the core of most investors' portfolios.
2.
Which is the better-diversified portfolio?
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It is not possible to determine which is better diversified. It depends on the funds. For example, if the 10-fund portfolio owns all large-cap growth funds and the two-fund portfolio contains a broad-based index fund and a bond fund, the latter would be more diverse. More funds doesn't necessarily mean more diversification.
3.
If you find that you need to take on a good deal more risk than you are comfortable with to reach a goal, which is not an option?
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Don't take on the risk and still plan to meet the goal. Investing is about compromise. You can't have everything. Low risk and high returns rarely go together.
4.
Noncore funds can add what to a portfolio?
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Both of the above. Core funds shouldn't be exciting. They should be what you think are reliable stock funds and bond funds. An increased return potential and variety should come from your noncore holdings. (Just remember: the potential for better returns also comes with other risks.)
5.
Why is it easier to stomach loss during long-term investing than it is during short-term investing?
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You have more time to make up the loss. As a general rule, you can recoup losses over a longer time period than a shorter one.